The purpose of this project is to develop theory for the interpretation of biomedical and chemical measurement techniques. At present we have worked on two such techniques: single-molecule spectroscopy (SMS) and optical spectroscopy applied to estimate optical tissue parameters to distinguish between normal and abnormal tissues. In the past year we have continued our development of the theory of SMS applied to two-state randomly interconverting systems. The theory of such systems has been developed, in which one rate constant fluctuates randomly in response to environmental fluctuations. We have also developed statistical theory for the error in estimates of rate constants in two-state systems. These estimates permit the experimenter to optimize such experiments insofar as is possible. The general theory has also been appliied to study techniques for parameter estimation in two-state systems in which resolution is so poor that the data is virtually uncorrelated. Using data provided by the laboratory of Dr. Sergey Bezrukov (NICHD) we have shown that an adaptation of our theory of two-state systems is able to deal very well with poor quality data. A second project is to develop a theoretical framework for optical imaging methods for biomedical applications. We are currently developing theory to characterize the trajectory of laser-injected photons in continuous wave reflectance measurements.